Chapter 6: Applications of Definite Integrals - Section 6.2 - Volumes Using Cylindrical Shels - Exercises 6.2 - Page 329: 3

$2 \pi$

We need to use the shell model as follows: $V=\int_p^{q} (2 \pi) \cdot (\space radius \space of \space shell) ( height \space of \space Shell) \space dy$ $ \implies V= \int_0^{\sqrt 2} (2 \pi) \cdot (y)(y^2) dy=2 \pi \times \int_0^{\sqrt 2} y^3 dy$ or, $=2\pi \times [\dfrac{y^4}{4}]_0^{\sqrt 2}$ or, $=2 \pi$